Lectures related to Dirac Delta Function

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Laplace Transform: Basics

Introduces Laplace transform, ROC, and LTI systems with transfer functions and frequency response.

Derivative of an Integral with Parameter

Covers deriving integrals with parameters and their derivatives, including special cases and proofs.

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Dirac Delta

Covers the definition and applications of the Dirac Delta function in signal processing.

Extreme Values and Constraints

Explores extreme values, constraints, Riemann's integral interpretation, and volume calculations of parallelipipeds in mathematics.

Fourier Transform: Motivating Formula

Covers the motivation behind the Fourier transform formula, explaining the process step by step.

Improper Integrals: Fundamental Concepts and Examples

Covers improper integrals, their definitions, properties, and examples in two and three dimensions.

Integration of CnR Class Functions

Explains the integration of Taylor series for CnR class functions.

Fourier Series: Convergence and Dirichlet Theorem

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

Volume Calculation: Two Cylinders Interaction

Explains the volume calculation by intersecting two cylinders using coordinates and integrals.

Derivative of an Integral

Covers the derivative of an integral dependent on a parameter and its fundamental properties.

Comparison Series and Integrals

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.

Green's Functions in Laplace Equations

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Calculus: Derivatives and Integrals

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Transforms of the Place

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Riemann Sphere: Correlations and Conditions

Covers the Riemann sphere, focusing on its conditions and correlation functions in mathematical and physical contexts.

Fourier Transform: Diffusion Equation

Explores the derivation of the diffusion equation using Fourier transforms and discusses the significance of Dirac delta functions in mathematical analysis.

Neural Signals and Signal Processing

Explores neural signals, EMG control, muscle synergies, and HD-EMG for prosthetic devices.